Compound Interest Formula and Concept
Compound Interest Meaning
When the amount after the first unit of time becomes the Principal for the second unit of time and so on, after fixing a certain unit of time, say yearly or half-yearly or quarterly to settle the previous amount.
This difference between the Amount and the Principal after a specified period is called Compound Interest.
Important Compound Interest Formula
- When the interest is compounded annually –
Amount = P{ \left( 1+\frac { R }{ 100 } \right) }^{ n }
- When the interest is compounded Half-yearly –
Amount = P{ \left( 1+\frac { R/2 }{ 100 } \right) }^{ 2n }
- When the interest is compounded quarterly –
Amount = P{ \left( 1+\frac { R/4 }{ 100 } \right) }^{ 4n }
- When the interest is compounded annually but time is in the fraction, say 3\frac { 3 }{ 5 } –
Amount = P{ \left( 1+\frac { R }{ 100 } \right) }^{ 3 }\times \left( 1+\frac { 3R/5 }{ 100 } \right)
- When rates are different for different years, say { R }_{ 1 },{ R }_{ 2 },{ R }_{ 3 } for Ist, 2nd, and 3rd year respectively-
Amount = P\left( 1+\frac { { R }_{ 1 } }{ 100 } \right) \left( 1+\frac { { R }_{ 2 } }{ 100 } \right) \left( 1+\frac { { R }_{ 3 } }{ 100 } \right)
Examples-
Q-1. Find the compound interest on Rs. 7500 at 4% p.a for two years compounded annually?
Solution-
Method-1(Using Formula)
Amount = [7500×(1 + 4/100)²] = (7500 × 26/25 × 26/25) = Rs. 8112
CI = 8112 – 7500 = Rs. 612
Method-2
Interest for first year since rate is annually, where P =7500, R = 4%, T = 1 year
Interest = (PRT/100) = (7500×4×1)/100 = 300
Now for the 2nd term
P = 7500 + 300 = 7800, R = 4%, T = 1 year
Interest = PRT/100 = (7800×4×1)/100 = 312
So, the total interest is 300 + 312 = Rs. 612